Content analysis findings

There has been much work done on commensurate and incommensurate frictional systems and friction anisotropy. When two surfaces are commensurate, their lattices match in perfect registry. Theoretically, it has been shown that commensurate systems can have as much as 14 orders of magnitude higher friction than corresponding incommensurate systems. The lower friction levels for incommensurate systems are due to the random positions of atoms with respect to each other on the mismatched lattices. Interfacial forces tend to cancel in this case, resulting in very low friction (Hirano et al.,1991; Shinjo and Hirano,1993). There are several experiments that reveal the effect of incommensurability on friction, although none have reported the phenomenal change in friction that is theoretically possible. Most of these studies focused on the adhesion and friction between like-materials or like-materials with similar lattice spacing and go from commensurate to

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incommensurate by rotating the lattices with respect to one another. For example, a surface force apparatus( SFA) was employed to study the adhesion of mica surface in distilled water and aqueous potassium chloride (KCl) (McGuiggan and Isrealachvili, 1990). The results related the adhesion of mica surfaces to the alignment of the mica surfaces with respect to one another. The adhesion peaked at θ = 0, 60, 120 and 180 degrees (θ = 0 corresponds to matching lattices), following the six-fold symmetry of the mica lattice. A related study of mica surfaces linked the friction of mica surfaces to their relative orientation, (Hirano et al., 1991).

Friction tester similar to a surface force apparatus (SFA) was used to rub two mica surfaces in both an argon-purged dry atmosphere with the surface temperature of the mica heated above 100^º C to prevent water adsorption. These measurements were then compared to ambient condition measurements with the mica surface temperatures held at 20ºC. In the argon-purged atmosphere, the friction reached maximum levels when the surfaces were commensurate (θ = 0, 60, 120 and 180 degrees, θ = 0 corresponds to matching lattices) and minimum levels, dropping by a factor of 4 when the surfaces were incommensurate (θ = 30, 90 etc). In ambient conditions, the original anisotropy disappeared, however owing to the adsorption of water and other contaminants onto the mica surfaces. The result lent support to the idea that frictional anisotropy is purely a surface effect

( Smith et al., 1996; Gyalog and Thomas, 1997).

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Scanning tunneling microscope (STM) was employed in utra-high vacuum to study the sliding of a tungsten wire tip surface on a planar silicon surface. Much like an AFM, the tungsten tip was rastered across the silicon surface and a displacement sensor was used to measure the bending of the tungsten wire caused by the friction between the two surfaces. Employing Hooke’s law to extract the frictional force from the displacement of the tungsten tip, it was found that the frictional force of the two surfaces in commensurate contact was 8 x 10^-8N. The friction vanished when the surfaces were in incommensurate contact, within their resolution. (The resolution of the instrument was 3x10^-9N). Not all friction anisotropy can be related to surface commensurability (Shinjo and Hirano, 1993).

In some experiments, friction anisotropy disappears at low loads when the surfaces are in elastic contact and is only present at high loads when the surfaces are in plastic contact. A typical example is an experiment that studied the friction between nickel (100) surfaces in UHV with and without adsorbed surface coatings of sulphur and ethanol (Hirano et al., 1991; Scharf et al., 1998). The adsorbed coatings modified the surface lattice of the bare nickel, the sulphur surface is well-ordered with lattice vectors rotated 45 degrees with respect to the bulk nickel, and the adsorbed ethanol is not ordered. The friction in this study was anisotropic and related to the bulk lattice structure of the nickel. The static friction coefficient was found to be minimized (lower by a factor of 3-4) at a bulk lattice mismatch of θ =

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45 degrees, regardless of the modifications to the surface by monolayer’s of atomic sulphur and up to 4 monolayers of adsorbed ethanol. Their results suggest that in some systems in plastic contact that the frictional anisotropy is related to deformation of the bulk material.

2.7: Static Friction

One of the most common everyday experiences with friction at the microscopic scale is the occurrence of static friction. The force to initiate motion (which itself is quite variable, depending for example on how long the two surfaces have been in contact) is virtually always larger than that required to keep an object in motion ( Eldrid et al., 2007). A closely associated phenomenon is that of stick – slip friction, whereby for certain sliding speeds, the velocity – weakening dependence of the transition from static to sliding friction leads to repetitive sticking and sliping at the interface, producing the all-too familiar screeching noises associated with brakes. Although static friction is ubiquitous, it is notoriously difficult to explain at the macroscopic and microscopic length scales ( Sundip et al., 2007; Suman et al., 2007).

Static friction and stick-slip motion are also familiar occurrences in nanotribology. Static friction has frequently been measured with surface force apparatus (SFA). Atomic scale stick-slip friction was first measured in the AFM by

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(Mate et al., 1987). Using an AFM with a tungsten probe on a graphite surface, it was found that the frictional force of the probe on the graphite had a periodicity of 2.5 angstroms, the same periodicity as the graphite surface. Since 1987, atomic scale stick-slip friction has been observed on many different materials

( Germann et al., 1993). Atomic scale stick-slip friction can be interpreted as the tip and sample remaining in the minimum potential energy position until a sufficiently strong shear stress is applied to force the tip to move (Carpick and Salmeron 1997). Interestingly, such stick-slip behaviour has always been observed to occur with the periodicity of the substrate lattice, even when the lattice points have multiple atoms. For example, it is not possible to differentiate between the molybdenum and the sulphur atoms in a MoS2 surface. The stick – slip periodicity measured by the LFM is 3.16 angstroms, which corresponds to the distance between MoS₂ molecules in the lattice (Fujisawa et al.,1994; Terada et al., 2000).

Static friction has never been evident in QCM measurements, both solid-solid and liquid – solid-solid interfaces being well described by the viscous friction law which is parameterized at low velocities by friction proportional to velocity, V.

Where V is the velocity of the object through the liquid. Given the differences in the sliding speeds, and geometries between QCM, SFA and AFM, there was some debate about the underlying reason for the lack of static friction in the QCM. A recent experiment explored this question (Mate et al., 1987). This experiment

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focused on the fact that while both QCM and SFA measurements of the shearing of the liquid films reveal friction, static friction is present only in the SFA geometry.

Employing a “blow-off experiment”, it was explored whether the open geometry or much greater shear rates of the QCM could account for the difference in the observed behaviours. Nitrogen was blown across a liquid film confined in a narrow channel. The laminar flow conditions generated a shear stress on the liquid film at shear rates comparable to those in the SFA. The results yielded viscous friction, so it was concluded that confined geometries and not the shear rates of the SFA and AFM resulted in static friction, while unconfined geometries like the QCM and the “blow-off” experiment are characterized by the viscous friction law.

The results are consistent with recent computer simulation experiments (Muser and Robbins, 2000). The effects that mobile atoms between two contacting crystalline surfaces have on friction were studied. As stated already, commensurate crystalline surfaces are expected to have high friction, and they exhibit static friction with or without contaminant atoms between the surfaces. Incommensurate crystalline surfaces, however, have very low friction. In the real world, however, almost all contacting surfaces are expected to be incommensurate, so the existence of static friction is difficult to explain. Simulations of modeled sub-monolayer and mobile contaminant films between two incommensurate surfaces were carried out.

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It was observed that the mobile molecules found small gaps between the surfaces.

Any sliding of the two surfaces will constrict or reduce the gaps in which the mobile molecules settle (Muser and Robbins, 2000). The molecules therefore resist sliding motion until the shear stress exceeds some threshold value and they

are displaced, resulting in the presence of static friction.

2.8: TOMLINSON MODEL

In Tomlinson model, the motion of the tip is influenced by both the interaction with the atomic lattice of the surface and the elastic deformations of the cantilever. The shape of the tip-surface potential v(r) depends on several factors such as the chemical composition of the materials in contact and the atomic arrangement of the tip end (Gnecco et al., 2010). First, we look at the analysis as a one dimensional case considering a sinusoidal profile with the periodicity of the atomic lattice a and a peak-to-peak amplitude E0. If the cantilever moves with a constant velocity v along the x-direction, the total energy of the system is

Etot (x,t) = cos + Keff (vt-x)² (2.3) K_{eff =} elastic spring constant, E₀ = maximum potential energy of the system.

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Fig. 2.4 shows the energy profile Etot (x,t) at two different instants.

Fig. 2.4. Energy profile experienced by FFM tip, (black circle) at t = o (dotted line) and t = t* (continuous line) (Gnecco et al., 2010).

When t = 0, the tip is localized in the absolute minimum of Etot. This minimum increases with time due to the cantilever motion until the tip position becomes unstable when t = t^* ( Gnecco et al., 2010). At a given time `t`, the position of the tip can be determined by equating to zero the first derivative of the expression Etot

(x,t) with respect to x to obtain

= sin - Keff (vt-x) = 0 (2.4)

The critical position x^* corresponding to t = t^* is determined by equating to zero the second derivative

to obtain x* =

arc cos (- ) (2.5)

y =

(2.6)

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The coefficient y compares the strength of the interaction between tip and surface with the stiffness of the system. When t = t^*, the tip suddenly jumps into the next minimum of the potential profile. The lateral force F*

which induces the jump is given by ( Gnecco et al, 2010) F^*=

a (2.7)

Thus the stick-slip is observed only if y >1 i.e when the system is not too stiff or the tip-surface interaction is strong enough (Gnecco et al., 2010).

Fig. 2.5 shows the lateral force FL as a function of the cantilever position, x.

Fig. 2.5. Friction loop obtained by scanning back and forth in the one-dimensional Tomlinson models. The effective spring constant Keff is the slope of the sticking part of the loop (if y>>1) (Gnecco et al., 2010).

When the cantilever is moved rightward, the lower part of the curve in Fig. 2.5 is obtained. If at a certain point, the cantilever’s direction of motion is suddenly inverted, the force has the profile shown in the upper part of the curve. The area of

FL (nN)

X (nm)

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the friction loop obtained by scanning back and forth gives the total energy dissipated (Gnecco et al., 2010).

Two-dimensional Tomlinson model:

In two dimensions, the energy of the system is given by

Etot (r,t) = U(r) + (vt-r)² (2.8)

where r = (x,y) and v is arbitrarily oriented on the surface.

Figure 2.6 shows the regions for a potential of the form represented by equation (2.8).

The tip follows the cantilever adiabatically as long as it remains in the (++) – region. When the tip is dragged to the border of the region it suddenly jumps into the next (++) – region (Gnecco et al., 2010).

Fig 2.6: Regions of the tip plane labeled according to the signs of the eigenvalues (Gnecco et al., 2010).

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In the above discussions we assumed that the tip is terminated by only one atom.

Let us consider the case of a periodic surface sliding on another periodic surface.

The atoms of one surface are harmonically coupled with their nearest neighbours, (Gnecco et al., 2010). We consider only the case of quadratic symmetries with lattice constants a1 and a2 for the upper and lower surfaces respectively. In such context, the role of commensurability is essential. Let the roots of the quadratic equation resulting from the quadratic symmetries be x1 and x2 , x1 greater than x2. In one-dimension, It was predicted that friction should decrease with decreasing commensurability, the minimum of friction being reached when

= x1

(

2.9) and maximum friction is obtained when

= x2 (2.10)

In two - dimension, the case of a1 = a2, was studied with a misalignment between the two lattices given by an angle .When the sliding direction changes, friction also varies from ` minimum value corresponding to the sliding angle = to a maximum value which is reached when = + . The misfit angle is related with commensurability (Bhushan, 2010). Since the misfit angles giving rise to commensurable structure form a dense subset, the dependence of friction on

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should be discontinuous. The numerical simulations performed by Gyalog are in agreement with the conclusion.

2.9: LINEAR COMBINATION OF ATOMIC ORBITALS.

Molecular orbitals were first introduced in 1927and 1928.

Linear combination of atomic orbitals (LCAO) was introduced in 1929 (Lernard-Jones, 1929 ). A ground-breaking paper presented by Lernard-Jones in 1929 showed how to derive the electronic structure of fluorine and oxygen molecules from quantum principles. This qualitative approach to molecular orbitals theory is part of the start of modern quantum science. A molecular orbital (MO) is a function describing the wave-like behaviour of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. Molecular orbitals are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule or other molecular orbitals from groups of atoms. Hence, molecular orbitals represent regions in a molecule where an electron is likely to be found. A molecular orbital can specify the electron configuration of a molecule, the spatial distribution and energy of one electron or a pair of electrons. A molecular orbital is represented as a linear combination of atomic orbitals

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(the LCAO-MO method). They are invaluable in providing model of bonding in molecules, understood through molecular orbital theory. Most present-day computational methods begin by calculating the MOs of the system. A molecular orbital describes the behaviour of one electron in the electric field generated by the nuclei and some average distribution of the other electrons (Kutzelnigg, 1996).

Molecular orbitals arise from allowed interactions between atomic orbitals, which are allowed if the symmetries (determined from group theory) of the atomic orbitals are compatible with each other. Efficiency of atomic orbital interactions is determined from the overlap (a measure of how well two orbitals constructively interact with one another) between two atomic orbitals which is significant if the atomic orbitals are close in energy. Molecular orbitals can be obtained from the linear combination of atomic orbitals. The number of molecular orbitals that form must equal the number of atomic orbitals in the atoms being combined to form the molecule. Linear combinations of atomic orbitals can be used to estimate the molecular orbitals that are formed upon bonding between the molecules constituent atoms. Similar to an atomic orbital, a Schrodinger equation which describes the behaviour of an electron can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wave- functions provide approximate solutions to the molecular Schrodinger equations.

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For simple diatomic molecules the obtained wavefunctions are represented mathematically by the equation (Lernard-Jones, 1929 )

Ψ = C_aψ_a + C_bψ_b (2.11)

ψ^* = Caψ_a – Cbψ_b, (2.12)

where ψ and ψ^* are the molecular wave functions for the bonding and anti-bonding molecular orbitals, respectively, ψ_a and ψ_b are the atomic wavefunctions from the atoms a and b, respectively, and Ca and Cb are adjustable coefficients. These coefficients can be positive or negative depending on the energies and symmetries of the individual atomic orbitals. As the two atoms come closer together their atomic orbitals overlap to produce areas of high electron density, and as a consequence, molecular orbitals are formed between the two atoms. The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals (Frexedas et al., 2002) .

2.10: BOND-ORBITAL MODEL

When atomic orbitals interact, the resulting molecular orbital can be

of three types: bonding, anti-bonding and nonbonding. Bonding interactions between atomic orbitals are constructive (in-phase) interactions. Bonding molecular orbitals are lower in energy than the atomic orbitals that combine to

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produce them. Anti-bonding interactions between atomic orbitals are destructive (out-of-phase) interactions. Anti-bonding molecular orbitals are higher in energy than the atomic orbitals that combine to produce them. Non-bonding molecular orbitals are the result of no interaction between atomic orbitals because of lack of compatible symmetries. Non-bonding molecular orbitals will have the same energy as the atomic orbitals of one of the atoms in the molecule

(Gary and Donald, 2004).

Later Harrison (Animalu, 1977) developed a new model of partial covalency in binary AB compounds starting from an atomic-like bond-orbital model rather than Philips band-like dielectric model. Harrison`s argument is that in the extreme ionic limit as one expects in large band gap instructors of the rock salt family like MgO having full inert gas configuration on the anion, a localized electron (bond) picture provide a more physical representation of the electronic states than the itinerant-electron (band) picture of the dielectric model. In the bond-orbital model, a hybrid orbital h^a is constructed from the atomic s and p orbitals centered on atom A and similar h^b is constructed from the atomic s and p orbitals centered

on atom B (Animalu, 1977).

h^a = (s^a + p^a ) (2.13) h^b = (s^b + p^b). (2.14)

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In terms of these, the two parameters of the model are defined namely the covalency energy (V2) and the polarity energy (V3) related to the ionicity energy but not equivalent to it given by

2V2 = - (<h^b|H|h^a > + < h^a |H|h^b>) (2.15) and

2V₃ = ( < h^b|H|h^b > - < h^a |H|h^a> ), (2.16)

where H is the one-electron Hamiltonian of the AB system. To relate V2 and V3 to the gap between bonding (valence) and anti-bonding (conduction) bands, we define the molecular orbitals

ψ_A = (h^a – ih^b), (2.17)

ψB = (ih^a + h^b) (2.18)

which are normalized and have an overlap with real and imaginary parts.

<ψA| ψB> = i (<h^a|h^a > - <h^b|h^b>) + (<h^a |h^b > + <h^b |h^a >) (2.19) If <h^a|h^a> = <h^b |h^b>, the imaginary (polar) term drops and we have

<ψA|ψB> = (<h^a|h^b> + <h^b|h^a >) (2.20)

But if <h^a|h^a> <h^b|h^b> then the overlap wave function contains both the polar and covalent components.

Then the energy gap

E_g = ( + )^½ (2.21)

is given by

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<ψ_A|H|ψ_B> = (<h^a|H|h^b> + <h^b|H|h^a>)

+ i(<h^a|H|h^a> - <h^b|H|h^b> ) = - (V2 + i V3) (2.22) In terms of these parameters, the fractional covalency ( c) and polarity (αp) are

α_c =

(2.23)

α_p =

(2.24)

and obey the relation

+ = 1 (2.25)

The ionicity fi of the dielectric model is related to αp by (Ammalu,1977)

f_i = 1 – (1- )^3/2 (2.26)

Two models – the valence bond model and the molecular orbital model (Kutzelnigg, 1996) were developed almost simultaneously. Linus Pauling became the champion of the valence bond model. This model is essentially a quantum mechanical version of the electron-dot model. It attempts to describe what orbitals are used by each atom when electrons are shared. For example when the simple molecule of hydrogen (H2) is formed from hydrogen atom, the valence bond model says that an s-orbital of one atom overlaps with an s-orbital of the other to form a bond. The molecular orbital model takes a different approach. It utilizes all of the orbitals on all of the atoms to generate a set of molecular orbitals.

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2.11: TEMPERATURE DEPENDENCE OF NANOTRIBOLOGY.

From Tomlinson model, at a given time t < t^*, the tip jump is prevented by the energy barrier E = E (Xmax, t) – E (Xmin, t), where Xmax. corresponds to the first maximum observed in the energy profile and X_min is the actual position of the tip.

The quantity E decreases with time or equivalently with the frictional force FL

until it vanishes when FL = F^*. Close to the critical point, the energy barrier can be written approximately as (Gnecco et al, 2010)

E =µ(F- FL) (2.27)

where F is close to the critical value F^* .

At finite temperature, the lateral force required to induce a jump is lower than F^*. To estimate the most probable value of FL at this point, we consider the probability

`P` that the tip does not jump. This probability changes with time `t` according to the master equation (Gnecco et al, 2010)

= - fo exp ( ) P(t) (2.28) where fo is the characteristic frequency of the system.

If time is replaced by the corresponding lateral force, the master equation becomes (Gnecco et al., 2010).

= - fo exp ( ) (P(FL) (2.29)

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The above equation shows that the probability of a tip jump is reduced at low temperatures T until it vanishes when T = 0. This predicts that friction should change with temperature. Using FFM, the effects of temperature on the nanotribology of n-hexadecane and octamethyllyclo-tetrasiloxane were studied.

The results in both cases show that nanotribology decreases with increase in temperature ( Bhushan, 2010).

The effect of temperature on friction and adhesion was studied using a thermal stage attached to the AFM. The friction force was measured at increasing temperature from 22 - 125°C. The results show that the increasing temperature causes a decrease of friction force adhesive force and coefficient of friction of Si(100), Z-15 (lubricant) and Z-DOL (BW) (lubricant) (Bhushan, 2010). This can be explained from the fact that at high temperature, desorption of water leads to the decrease of friction force, adhesive force and coefficient of friction of all the samples. Besides that, the reduction of surface tension of water also contributes to the decrease of friction and adhesion. For Z-15 film, the reduction of viscosity at high temperature has an additional contribution to the decrease of friction. In the case of Z-DOL (BW) film, molecules are more easily oriented at high temperature which may also be responsible for the low friction. Using a surface force apparatus, it has been shown that a change in temperature induces phase

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transformation (from crystalline, solid-like to amorphous, liquid like) in surfactant monolayers, which are responsible for the observed changes in friction force.

Tomlinson`s model was used to study the temperature dependence of nanotribology on n-hexadecane and octamethycyclotetrasiloxane and in each case, the results show that friction force decreases as temperature increases,

(Gnecco et al, 2010). The effects of temperature on viscosity of silica was studied.

The experimental results show that viscosity decreases as temperature increases.

The effects of temperature on nanotribology of sodium chloride, NaCl (001) was studied using FFM with silicon tip. The measurement was carried out under ultrahigh vacuum and low temperature regime. The results indicate that nanotribology decreases with increase in temperature (Krylov and Frenken, 2014).

Hence at low velocity regime, temperature acts as a lubricant. Thermally activated stick-slip results in a strong decrease of nanotribology with increase in temperature. A significant decrease of nano-friction with increase in temperature was observed in a series of AFM measurements on graphite in ultrahigh vacuum (UHV) conditions and in a wide temperature range (140-750k) (Gnecco and Meyer, 2015). In another series of UHV experiments, the temperature dependence of nanotribology was measured from cryogenic conditions to a few hundred Kelvin for silicon, silicon carbide (SiC), ionic crystals and graphite. The results indicate

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that nanotribology decreases with increase in temperature (Gnecco and Meyer, 2015).

2.12: VELOCITY DEPENDENCE OF NANOTRIBOLOGY

Velocity dependence of nanotribology was studied using FFM. It was observed that friction between silicon tips and diamond, graphite or amorphous carbon is constant with scan velocities of few μm/s. In experiments on lipid films on mica, a range of velocities from 0.01 to 50 m/s was explored and a critical velocity Vc = 3.5 m/s was found which discriminates between an increasing friction and a constant friction (Liu and Bhushan, 2004).

In investigating the velocity effect on nanotribology, the friction force versus normal load relationships of Si (100), Z-15 and Z-DOL (BW) at different velocities were measured (Bhushan, 2010; Sundararajan and Bhushan, 2000). The results indicate that for silicon wafer, the friction force decreases logarithmically with increasing velocity. For Z-15, the friction force decreases with increasing velocity up to 10 m/s after which it remains almost constant. The velocity has a much smaller effect on the friction force of Z-DOL (BW). It reduced slightly only at very high velocities. The results also indicate that the adhesive force of Si (100) is increased when the velocity is higher than10 m/s. The adhesive force of Z-15 is reduced dramatically when the velocity increased up to 20 m/s, after which it is reduced slightly. The adhesive force of Z-DOL (BW) also decreased at high

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velocity. In the testing range of velocity, only the coefficient of friction of Si (100) decreases with velocity, but the coefficient of friction of Z-15 and Z-DOL (BW) almost remain constant. This implies that the friction mechanism of 15 and Z-DOL (BW) do not change with variations in velocity. The mechanisms of the effect of velocity on the adhesions and friction are explained based on the tribochemical reactions. For Si (100), tribochemical reaction plays a major role.

Although at high velocity, the meniscus is broken and does not have enough time to rebuild, the contact stresses and high velocity lead to tribochemical reactions of Si (100), water and Si3 N4 tip, which have native oxide (SiO2) layers with wafer molecule ( Gnecco et al., 2010). The following reactions occur.

SiO2 + 2H2O Si (OH)4 (2.30)

S i3 N4 + 16H2O Si3 (OH)4 + 4(NH4O3H3) (2.31)

The Si(OH)₄ is removed and continuously replenished during sliding. The Si(OH)₄ layer between the tip and Si (100) surface is known to be of low shear strength and causes a decrease in friction force and coefficient of friction in the lateral direction.

The chemical bonds of SiOH between the tip and Si (100) surface induce large adhesive force in the normal direction. For Z-15 film, at high velocity, the meniscus formed by condensed water and Z-15 films molecules is broken and does not have enough time to rebuild. Therefore the adhesive force and consequently, the friction force is reduced. For Z-DOL (BW) film, the surface can absorb few

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water molecules in ambient condition and at high velocity. These molecules are displaced which is responsible for a slight decrease in friction force and adhesive force. Even at high velocity range, the friction mechanisms for Z-15 and Z-DOL (BW) films still are shearing of the viscous liquid and molecular orientation, respectively. Thus the coefficients of friction of Z-15 and Z-DOL (BW) do not change with velocity. It was suggested that in the case of samples with mobile films, such as condensed water and Z-15 films, alignment of liquid molecules (shear thinning) is responsible for the drop in friction force with an increase in scanning velocity. This could be another reason for the decrease in friction force with velocity for Si(100) and Z-15 film in the study (Bhushan and Liu, 2004).

Experiments have demonstrated that capillary condensation can lead to a logarithmic decrease of nano-friction with increasing velocity (Krylov and Frenken, 2014). This has been interpreted as the consequence of the thermally activated nucleation of water bridges between tip and sample asperities, in a dynamics that somewhat resembles the velocity weakening observed in macroscale contacts. Measurements of nanotribology of surfaces modified so that they can form hydrogen-bonding networks also show a reduction of nano-friction with increasing sliding velocity which has been explained analogously, in terms of the formation and rupture of these bonding networks (Krylov and Frenken, 2014).

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The variation of nano-friction as a function of sliding velocity was studied using AFM with silicon tip on NaCl (100). Under a humid environment, nanotribology decreases with increase in velocity (Gnecco and Meyer, 2015). This can be attributed to the formation of water menisci by thermally activated capillary condensation. This decrease of nano-friction with velocity increase can also be associated with chemical modifications. This happens in systems forming cross-links structure that can be broken by the applied load, such as surfaces terminated by -OH,-COOH and -NH2 groups. At slow velocities, there is more time to form bonds between tip and surface, which results in larger nano-friction (Gnecco and Meyer, 2015). If the scan velocity increases, thermally activated processes are less important, and beyond a critical value, the nano-friction becomes independent of the velocity as seen in a series of measurements between silicon tips and diamond, graphite and amorphous carbon surfaces with scan velocities above 1µm/s (Gnecco and Meyer, 2015). The dependence of nanotribology on the sliding velocity was studied using AFM tip sliding on graphene membrane. The results show that nanotribology increases with decrease in velocity (Sandoz-Rosado, 2013).

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2.13: LOAD DEPENDENCE OF NANOTRIBOLOGY

When there is no adhesive force between two surfaces, the only attractive force that needs to be overcome for sliding to occur is the externally applied load or pressure. It is instructive to compare the magnitudes of the externally applied pressure to the internal Van der Waals pressure between two smooth surfaces. The internal Van der waals pressure between two flat surfaces is given by

P =

(2.32)

Using a typical Hamaker constant of A_H = 10^-19 J and assuming D_o = 2nm for the equilibrium interatomic spacing we have P = 1 GPa (10⁴ atm.) (Isrealachvili and Ruths, 2010).

This implies that we should not expect the externally applied load to affect the interfacial friction force until the externally applied load begins to exceed

100MPa (10³ atm). This is in agreement with experimental data where the effect of load became dominant at pressures in excess of 10³atm. This actually implies that the effect of normal load on nano-friction becomes dominant at high values of load (Isealachvili and Ruths, 2010). Nanotribological properties of Si (100), Z-15 and Z-DOL (BW) films on silicon (100) was investigated. The friction force versus normal load curves were measured by making friction force measurements at increasing normal loads (Liu and Bhushan, 2004). The results obtained for silicon (100), Z-15 and Z-DOL (BW) films on Si (100) are shown in Fig. 2.7.

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Fig 2.7: Friction force versus normal load curves for Si (100), 2.8nm – thick, Z-15 film and 2.3nm-thick Z-DOL (BW) film at 2 m/s and in ambient air sliding against a Si3N4 tip (Liu and Bhushan, 2004).

An approximately liner response of all three samples is observed in the load range of 5-130nN. The friction force of solid-like Z-DOL (BW) is consistently smaller than that for Si (100), but the friction force of liquid – like Z-15 lubricant is higher than that of Si (100). In the above figure the nonzero value of friction force at zero external load is due to the adhesive forces ( Liu and Bhushan, 2004). The static friction force of silicon micromotors lubricated with Z-DOL was studied using AFM. It was found that liquid-like lubricants of Z-DOL significantly increases the static friction force whereas solid-like Z-DOL (BW) coating can dramatically reduce the static friction force. In both cases, the results show that friction increases with increase in normal load (Sundararajan and Bhushan, 2001).

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Friction versus load in ambient air (RH-55%) was measured with a silicon tip on C6o islands grown on a germanium sulphide (GeS) substrate. Since the C6o

coverage was incomplete, the experiment on friction measurements was performed with the same tip on both the GeS and the C6o surfaces together

(Carpick and Salmeron, 1997). In both cases, the results show that friction increases with increase in normal load. The load dependence on nanotribology of C6o was studied using atomic force microscope at different temperatures. The results show that nanotribology increases with increase in normal load (Liang et al., 2003). The effects of normal load on nanotribology of sodium chloride NaCl(001) was studied using FFM with silicon tip. The results show that nanotribology increases with increase in normal load (Krylov and Frenken, 2014).

Their results also show that nano- friction nearly disappears at low loads.

The general trend observed in AFM experiments is that nanotribology increases with increase in normal load (Gnecco and Meyer, 2015). A linear load dependence of nanotribology was reported on various substrates including gold and alkylthiol molecules (Gnecco and Meyer, 2015). The variation of friction with normal load for aluminum pair, copper pair and aluminum-brass pair were studied. The results show that friction coefficient increases with increase in normal load. This may be due to increase in the adhesion strength, (Nuruzzaman and Chowdhury, 2012). At low loads, the oxide film effectively

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separates two metal surfaces and there is little or no true metallic contact, hence, the friction coefficient is low. At higher load conditions, the film breaks down resulting in intimate metallic contact which is responsible for higher friction, (Nuruzzamn and Chowdhury, 2012). Effects of normal load on nanotribology of various forms of human hair were studied using AFM. The results indicate that nanotribology increases with increase in normal load (Bhushan and La Torre, 2010). Normal load dependence of nanotribology was studied for silicon dioxide (SiO2) and graphene using AFM. The results show that nanotribology increases with increase in normal load with graphene having low friction when compared to silicon dioxide substrate (Sandoz-Roszdo, 2013).

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